In this problem, we are tasked with determining the values of x for which the function f(x) is positive. We have been provided a graphical representation of the function, and we will use this graph to find our solution.
1. Restate the problem: We need to find all values of x where the function f(x) is greater than zero, based on its graphical representation.
2. Identify key information: The graph is typically that of some function f(x). The graph shows points and lines that illustrate where the function is above and below the x-axis. Points or curves on or above the x-axis indicate positive values.
3. Potential approach: Analyze where the graph is above the x-axis.
5. The most appropriate approach is to visually inspect the graph to identify when the curve is above the x-axis.
6. Steps needed:
- Identify any turning points or intersections with the x-axis.
- Determine the segments of the x-axis where the function is above it.
8. Simplify the inspection by focusing on intervals separated by intersections with the x-axis.
9. Consider that the function might only touch the x-axis at specific points, like at roots, and analyze behavior around these points.
Based on the graph, we observe the following behavior of the function f(x):
The function intersects the x-axis at x=−4. This indicates a potential root or turning point where the function transitions from positive to negative or vice versa.
From the graph, it appears that the function is above the x-axis on both sides of x=−4, except exactly at x=−4, where it touches the x-axis.
Hence, the function f(x) is positive for x>−4 and for x<−4. Note that exactly at x=−4, the function is zero, not positive.
Therefore, the solution is: x>−4 or x<−4.
In conclusion, the function f(x) is positive for these values of x, except the point where it touches the x-axis.
The corresponding choice given the problem's options is: